Monday, July 5, 2021

Police Shootings: Statistics, Opinions, and Game Theory


After the death of Mr. George Floyd at the hands of Minneapolis police officers, the press emphasis on the race of the victim was immediate.  The death was, to many, confirmation that that there was a consistent pattern of biased treatment of black individuals in encounters with law enforcement.  The Floyd incident did not involve a shooting; Mr. Floyd died while being restrained through a knee-hold by the involved officer.  Nonetheless, press accounts tended to conflate the event with the police shootings issue.  


The event sparked protests and riots in 550 cities and damages (according to insurers) of $1 billion or more.  Although the cruelty of the Floyd event may have been enough to spark such a response, it seems likely that the representation of police shootings as evidence of persistent and structural racial bias played a key part.  The press accounts of the statistics of policy shootings was draw from numerous sources, but relied significantly on the use of the Washington Post (WP) newspaper’s shootings database.  For example, the infographic in Figure 1 was produced and widely disseminated by the Statista service.  It used data from the Washington Post shootings database from 2015 through May 28, 2020.  

Figure 1.  Infographic on U.S. Police Shooting rates, by Race, June 2020


As the graphic indicates, the total number of police shooting deaths, by race, in the 2015 to 2020 time span of the database, averaged approximately 1,000 per year.  Notably, there were almost twice as many White as Black shooting victims.  However, Statista normalized the rates across race by dividing the absolute number of deaths by the estimated population of each.  The graphic then reports the rate on a per million population basis.  (Note:  Statista allows reproduction of its infographics as long as proper attribution is made to the company.)

As a result, the rate for Black victims is nearly three times that of White persons and almost 50 percent larger than for Hispanic persons.  Although use of a per capita or population averaging scheme is common, it is usually employed when population is the factor most likely to generate variation that needs to be accounted for.  For example, when studying the importance of the restaurant industry by city, it makes sense to adjust for the size of the individual cities’ by population.  This is because population is likely a main determinant of demand for restaurant services.  


This is not so in the context of police shootings.  Police actions occur in the setting of violent activity and affect very specific populations.  That is why the per capita involvement in violent victimization settings is very different by race, as revealed by the violent victimization survey of the Bureau of Justice statistics (BJS).  


According to the 2010 to 2015 BJS survey, the per capita violent crime rate—the number of violent crimes committed by persons of a given race divided by its population—is very different by race.  That of Blacks is 950 percent that of Whites.  That of Hispanics is about 140 percent of that of Whites.  This is contrary to the measure presented in Figure 1 which implicitly assumes that police contact with the citizenry is random across the entire population.  When this is incorporated in an infographic such as Figure 1, a very different picture inevitable emerges.  Specifically, it appears that almost exactly one person is killed for every thousand persons of a given race, irrespective of whether their race is Black, White or Hispanic.  


Figure 2.  U.S. Police Shooting rates, by Crime Rate by Race, June 2020


This result is contrary to the widely accepted notion represented in Figure 1 which implies a significant tendency toward police shooting of black individuals.  It is likely that the Statista analysis, which likely was widely used in press reporting and internet communications, amplified the stereotype of police bias against minorities.  The simple per capita approach is commonly used by others, such as PoliceScoreCard.org (2021).  


The Statista analysis, by using a simple, population adjustment to the raw statistics, is of no practical use in evaluating the underlying issue of racial disparity in police shootings.  The implication of Figure 2 is that the crime rate—by itself— is an important determinant of police behavior.  The finding of a nearly identical shooting rate by race across the three races says that evidence of racial bias in police shootings has to be sought elsewhere. 


To that point, there are other studies that report finding bias using other data or using other methods, such as Ross (2015).  Other studies focus on other dimensions of the interactions of civilians with the police, such as vehicle stops and searches, use of handcuffs, use of non-lethal methods, and specific circumstances such as whether the civilian was armed or not.  There are also studies that use shootings data that report finding little or no bias, such as Johnson et al. (2019), and when police decisions to shoot are studied via simulations, such as Correll et al. (2007).  


The ambiguous state of the literature is because of the ambiguous nature of the phenomena being studied.  An encounter of a civilian and a police officer is a classic instance of what economists call a “game theory” problem.  Specifically, an active encounter of a putative criminal with police puts the two parties in a setting that triggers brinkmanship behavior.  The putative criminal has a goal of besting the police in order to gain a positive outcome (getting away with a monetary reward or freedom from some punishment), while the police hopes to best the criminal and thereby be rewarded by preserving personal or citizen safety, life or property.


The escalation of effort is the path to one party prevailing.  However, this escalation is what makes extreme outcomes like killing your opponent likely.  This is because neither party understands fully (a) what the other party has at stake or (b) how extreme the other party will act.  As the economists Dixit and Nalebuff point out in their research on strategic behavior, this uncertainty or risk raises the likelihood of catastrophic events even when the mutual intent of the parties is to act rationally.  Put differently, the two parties have to use what information they have or can detect in the behavior of the other to disambiguate what is likely to happen.


It is naïve to think that the parties lack some statistical opinion of the likely behavior or capabilities of the other.  The dramatically higher violent crime rate of Blacks is part of the statistical baggage that police bring to the encounter, leading to an expectation of a more difficult interaction.  Similarly, if the surveys by the Gallup Center on Black Voices are accurate, Blacks have a 50 percent higher probability than Whites of having experienced police in their neighborhood, and fewer than 1 in 5 expects to be treated respectfully (versus 56 percent of Whites).  Thus, both parties are arguably in an already-escalated, defensive state when the encounter occurs.  


The implications for policy are not trivial.  Both groups have to exhibit different behaviors so that more conciliatory interactions are expected of each other.  The work of Corman et al. (2002) and Miller et al. (2004) using the experience of New York City in the 1990s is that increased police presence can provide both better service to the community and improve mutual familiarity of citizens and police.  


The one policy that seemingly will absolutely nothelp in this regard is unfunding and reducing police presence.  The surveys done by Gallup's Center on Black Voices reveal that, though there are important trust issues to resolve, most Blacks value a police presence.  Indeed, the Gallup survey report by Saad (2020) reveals that fully 81 percent of Blacks desire the same or greater police presence.  Unfortunately, the current unfunding programs seem to aggravate neighborhood crime levels and discourage retention of all police staff, including those for whom better community relationship development would be welcome.    


Sources:


Ross CT (2015) A Multi-Level Bayesian Analysis of Racial Bias in Police Shootings at the County-Level in the United States, 2011–2014. PLoS ONE 10(11): e0141854. doi:10.1371/journal. pone.0141854 


D. J. Johnson, T. Tress, N. Burkel, C. Taylor, J. Cesario, Officer characteristics and racial disparities in fatal officer-involved shootings. Proc. Natl. Acad. Sci. U.S.A. 116, 15877–15882 (2019)


https://policescorecard.org, July 2021.   “Key Findings, 8,768 killings by police, Based on population, a Black person was 2.9x as likely and a Latinx person was 1.4x as likely to be killed by police as a White person in America from 2013-20.  


Joshua Correll, Bernadette Park, Charles M Judd, Bernd Wittenbrink, Melody S Sadler, and Tracie Keesee, “Across the thin blue line: police officers and racial bias in the decision to shoot 

“ J Pers Soc Psychol. June 2007.


Avinash K. Dixit and Barry J. Nalebuff: Thinking Strategically, W.W Norton, pp. 205–222 (1991).


Saad, Lydia, “Black Americans Want Police to Retain Local Presence,” Gallup Center on Black Voices, August 5, 2020


Corman, Hope and Naci Mocan, “Carrots, Sticks and Broken Windows,” NBER Working Paper No. 9061 July 2002 


Miller, Joel, Robert C. Davis, Nicole J. Henderson, John Markovic, Christopher W. Ortiz, “Public Opinions of the Police: The Influence of Friends, Family, and News Media,” an independent report to the US Institute of Justice, May 2004 2001-IJ-CX-0038